On orbifolds and free fermion constructions

TL;DR

This paper establishes a detailed correspondence between orbifold constructions and free fermion models in string theory, classifying certain orbifolds and analyzing their geometric and non-geometric nature.

Contribution

It provides a complete classification of orbifolds formed from products of elliptic curves and abelian groups, linking them to free fermion models and identifying cases with geometric interpretations.

Findings

Classified orbifolds X/G with elliptic curve products and abelian twists.

Identified geometric interpretations for certain orbifolds, including Borcea-Voisin threefolds.

Proved the non-geometric nature of the semi-realistic NAHE free fermion model.

Abstract

This work develops the correspondence between orbifolds and free fermion models. A complete classification is obtained for orbifolds X/G with X the product of three elliptic curves and G an abelian extension of a group (Z_2)^2 of twists acting on X. Each such quotient X/G is shown to give a geometric interpretation to an appropriate free fermion model, including the geometric NAHE+ model. However, the semi-realistic NAHE free fermion model is proved to be non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In particular cases it is shown that X/G can agree with some Borcea-Voisin threefolds, an orbifold limit of the Schoen threefold, and several further orbifolds thereof. This yields free fermion models with geometric interpretations on such special threefolds.